Statistical Graphics for High-Dimensional Data
Susan VanderPlas
Statistics Department
Iowa State University
Does this data have homogeneous variance?
Do any of these plots have homogeneous variance?
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Which Plot has Homogeneous Variance?
Sine Illusion
Sine Illusion - Explained
Perception is optimized for three dimensions.
Our brains sometimes inappropriately apply 3d heuristics to 2d images, producing optical illusions.
Sine Illusion
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Solution 1: Transform X
From: Signs of the Sine Illusion: Why we need to care (JCGS, 2015)
\((f \circ T)(x) = a + (b-a)\left(\int_{a}^x |f^\prime(z)| dz\right)/\left(\int_{a}^{b}|f^\prime(z)| dz\right)\) \((f \circ T_w)(x) = (1-w) \cdot x + w \cdot (f \circ T)(x)\)
Solution 2: Transform Y
From: Signs of the Sine Illusion: Why we need to care (JCGS, 2015)
\(l_{new}(x_0) = l_{old} \sqrt{1 + f^\prime(x_0)^2}\) \(l_{new_w}(x) = (1-w) \cdot l_{old} + w \cdot l_{new}(x)\)
Experimental Validation
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Results
- Histograms show estimated parameter values
- Lines show individual estimated values
- w=0 and w=1 (fully corrected) are not acceptable weights.
- Weight values are similar across correction type and individual
Visualizing SNPs:
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Huge number of interesting genes (70 million ID’d SNPs)
Applet Design
SNP Population Distribution
Density of SNPs: Chromosome Level
Individual SNPs: Comparing Varieties
Genealogy and Phenotypes
Interactive Plot Design
Goal: Understand which features are most visually important.
Goal: Understand which features are most visually important.
Visual Reasoning
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Visual Reasoning
Conclusion: Lineups are an inductive classification task using graphics; performance is not seriously impacted by spatial ability (outside of general aptitude).
Graphical Features
Goal: Understand which features are most visually important.
Graphical Features
Goal: Understand which features are most visually important.